Deck 7: Linear Programming Models: Graphical and Computer Methods

Question 1

Any time that we have an isoprofit line that is parallel to a constraint,we have the possibility of multiple solutions.

Answer 1

True

Question 2

In the term linear programming,the word programming comes from the phrase "computer programming."

Answer 2

False

Question 3

One of the assumptions of LP is "simultaneity."

Answer 3

False

Question 4

The solution to a linear programming problem must always lie on a constraint.

Question 5

The term surplus is associated with ≥ constraints.

Question 6

Resource mix problems use LP to decide how much of each product to make,given a series of resource restrictions.

Question 7

One of the assumptions of LP is "proportionality."

Question 8

In some instances,an infeasible solution may be the optimum found by the corner point method.

Question 9

In a linear program,the constraints must be linear,but the objective function may be nonlinear.

Question 10

Any linear programming problem can be solved using the graphical solution procedure.

Question 11

An LP formulation typically requires finding the maximum value of an objective while simultaneously maximizing usage of the resource constraints.

Question 12

The set of solution points that satisfies all of a linear programming problem's constraints simultaneously is defined as the feasible region in graphical linear programming.

Question 13

The term slack is associated with ≥ constraints.

Question 14

There are no limitations on the number of constraints or variables that can be graphed to solve an LP problem.

Question 15

The rationality assumption implies that solutions need not be in whole numbers (integers).

Question 16

Management resources that need control include machinery usage,labor volume,money spent,time used,warehouse space used,and material usage.

Question 17

The existence of non-negativity constraints in a two-variable linear program implies that we are always working in the northwest quadrant of a graph.

Question 18

The shadow price is the same as the dual price in maximization problems.

Question 19

An objective function is necessary in a maximization problem but is not required in a minimization problem.

Question 20

Resource restrictions are called constraints.

Question 21

Consider the following linear programming problem: The maximum possible value for the objective function is

A)360.
B)480.
C)1520.
D)1560.
E)None of the above

Question 22

Consider the following linear programming problem: Which of the following points (X,Y)is not a feasible corner point?

A)(0,60)
B)(105,0)
C)(120,0)
D)(100,10)
E)None of the above

Question 23

Which of the following is not a property of linear programs?

A)one objective function
B)at least two separate feasible regions
C)alternative courses of action
D)one or more constraints
E)objective function and constraints are linear

Question 24

Which of the following is not a part of every linear programming problem formulation?

A)an objective function
B)a set of constraints
C)non-negativity constraints
D)a redundant constraint
E)maximization or minimization of a linear function

Question 25

Consider the following linear programming problem: The feasible corner points are (48,84), (0,120), (0,0), (90,0).What is the maximum possible value for the objective function?

A)1032
B)1200
C)360
D)1600
E)None of the above

Question 26

The addition of a redundant constraint lowers the isoprofit line.

Question 27

Typical resources of an organization include

A)machinery usage.
B)labor volume.
C)warehouse space utilization.
D)raw material usage.
E)All of the above

Question 28

Infeasibility in a linear programming problem occurs when

A)there is an infinite solution.
B)a constraint is redundant.
C)more than one solution is optimal.
D)the feasible region is unbounded.
E)there is no solution that satisfies all the constraints given.

Question 29

Which of the following is not a property of all linear programming problems?

A)the presence of restrictions
B)optimization of some objective
C)a computer program
D)alternate courses of action to choose from
E)usage of only linear equations and inequalities

Question 30

A widely used mathematical programming technique designed to help managers and decision making relative to resource allocation is called

A)linear programming.
B)computer programming.
C)constraint programming.
D)goal programming.
E)None of the above

Question 31

The mathematical theory behind linear programming states that an optimal solution to any problem will lie at a(n)________ of the feasible region.

A)interior point or center
B)maximum point or minimum point
C)corner point or extreme point
D)interior point or extreme point
E)None of the above

Question 32

The corner point solution method

A)will always provide one,and only one,optimum.
B)will yield different results from the isoprofit line solution method.
C)requires that the profit from all corners of the feasible region be compared.
D)requires that all corners created by all constraints be compared.
E)will not provide a solution at an intersection or corner where a non-negativity constraint is involved.

Question 33

Sensitivity analysis enables us to look at the effects of changing the coefficients in the objective function,one at a time.

Question 34

When two or more constraints conflict with one another,we have a condition called unboundedness.

Question 35

When appropriate,the optimal solution to a maximization linear programming problem can be found by graphing the feasible region and

A)finding the profit at every corner point of the feasible region to see which one gives the highest value.
B)moving the isoprofit lines towards the origin in a parallel fashion until the last point in the feasible region is encountered.
C)locating the point that is highest on the graph.
D)None of the above
E)All of the above

Question 36

If the isoprofit line is not parallel to a constraint,then the solution must be unique.

Question 37

A feasible solution to a linear programming problem

A)must be a corner point of the feasible region.
B)must satisfy all of the problem's constraints simultaneously.
C)need not satisfy all of the constraints,only the non-negativity constraints.
D)must give the maximum possible profit.
E)must give the minimum possible cost.

Question 38

The simultaneous equation method is

A)an alternative to the corner point method.
B)useful only in minimization methods.
C)an algebraic means for solving the intersection of two or more constraint equations.
D)useful only when more than two product variables exist in a product mix problem.
E)None of the above

Question 39

When a constraint line bounding a feasible region has the same slope as an isoprofit line,

A)there may be more than one optimum solution.
B)the problem involves redundancy.
C)an error has been made in the problem formulation.
D)a condition of infeasibility exists.
E)None of the above

Question 40

In a maximization problem,when one or more of the solution variables and the profit can be made infinitely large without violating any constraints,the linear program has

A)an infeasible solution.
B)an unbounded solution.
C)a redundant constraint.
D)alternate optimal solutions.
E)None of the above

Question 41

The difference between the left-hand side and right-hand side of a greater-than-or-equal-to constraint is referred to as

A)surplus.
B)constraint.
C)slack.
D)shadow price.
E)None of the above

Question 42

If the addition of a constraint to a linear programming problem does not change the solution,the constraint is said to be

A)unbounded.
B)non-negative.
C)infeasible.
D)redundant.
E)bounded.

Question 43

A constraint with positive slack or surplus is called a

A)nonbinding constraint.
B)resource constraint.
C)binding constraint.
D)nonlinear constraint.
E)linear constraint.

Question 44

If one changes the contribution rates in the objective function of an LP,

A)the feasible region will change.
B)the slope of the isoprofit or isocost line will change.
C)the optimal solution to the LP is sure to no longer be optimal.
D)All of the above
E)None of the above

Question 45

Two models of a product - Regular (X)and Deluxe (Y)- are produced by a company.A linear programming model is used to determine the production schedule.The formulation is as follows: The optimal solution is X = 100,Y = 0. How many units of the regular model would be produced based on this solution?

A)0
B)100
C)50
D)120
E)None of the above

Question 46

A straight line representing all non-negative combinations of X₁ and X₂ for a particular profit level is called a(n)

A)constraint line.
B)objective line.
C)sensitivity line.
D)profit line.
E)isoprofit line.

Question 47

Consider the following linear programming problem: Which of the following points (X,Y)is not feasible?

A)(50,40)
B)(20,50)
C)(60,30)
D)(90,10)
E)None of the above

Question 48

Which of the following is not an assumption of LP?

A)simultaneity
B)certainty
C)proportionality
D)divisibility
E)additivity

Question 49

Two models of a product - Regular (X)and Deluxe (Y)- are produced by a company.A linear programming model is used to determine the production schedule.The formulation is as follows: The optimal solution is X = 100,Y = 0. Which of these constraints is redundant?

A)the first constraint
B)the second constraint
C)the third constraint
D)All of the above
E)None of the above

Question 50

The coefficients of the variables in the constraint equations that represent the amount of resources needed to produce one unit of the variable are called

A)technological coefficients.
B)objective coefficients.
C)shadow prices.
D)dual prices.
E)None of the above

Question 51

Consider the following linear programming problem: What is the optimum solution to this problem (X,Y)?

A)(0,0)
B)(50,0)
C)(0,100)
D)(400,0)
E)None of the above

Question 52

Sensitivity analyses are used to examine the effects of changes in

A)contribution rates for each variable.
B)technological coefficients.
C)available resources.
D)All of the above
E)None of the above

Question 53

Which of the following is not acceptable as a constraint in a linear programming problem (maximization)?

A)Constraint 1
B)Constraint 2
C)Constraint 3
D)Constraint 4
E)None of the above

Question 54

Consider the following linear programming problem: This is a special case of a linear programming problem in which

A)there is no feasible solution.
B)there is a redundant constraint.
C)there are multiple optimal solutions.
D)this cannot be solved graphically.
E)None of the above

Question 55

Sensitivity analysis may also be called

A)postoptimality analysis.
B)parametric programming.
C)optimality analysis.
D)All of the above
E)None of the above

Question 56

The difference between the left-hand side and right-hand side of a less-than-or-equal-to constraint is referred to as

A)surplus.
B)constraint.
C)slack.
D)shadow price.
E)None of the above

Question 57

Consider the following linear programming problem: This is a special case of a linear programming problem in which

A)there is no feasible solution.
B)there is a redundant constraint.
C)there are multiple optimal solutions.
D)this cannot be solved graphically.
E)None of the above

Question 58

A constraint with zero slack or surplus is called a

A)nonbinding constraint.
B)resource constraint.
C)binding constraint.
D)nonlinear constraint.
E)linear constraint.

Question 59

Which of the following is a basic assumption of linear programming?

A)The condition of uncertainty exists.
B)Independence exists for the activities.
C)Proportionality exists in the objective function and constraints.
D)Divisibility does not exist,allowing only integer solutions.
E)Solutions or variables may take values from -∞ to +∞.

Question 60

The condition when there is no solution that satisfies all the constraints simultaneously is called

A)boundedness.
B)redundancy.
C)optimality.
D)dependency.
E)None of the above

Question 61

What is the increase in the objective value if 2 units of extrusion are added?

A)3
B)6
C)48
D)96
E)Not enough information provided

Question 62

Which of the following is not acceptable as a constraint in a linear programming problem (minimization)?

A)Constraint 1
B)Constraint 2
C)Constraint 3
D)Constraint 4
E)Constraint 5

Question 63

Consider the sensitivity report below for the problems which follow.
The optimal solution to this linear program is

A)x1 = 0,x2 = 0.
B)x1 = 34,x2 = 40.
C)x1 = 6,x2 = 11.
D)x1 = 7.33,x2 = 6.
E)x1 = 3,x2 = 6.

Question 64

What type of problems use LP to decide how much of each product to make,given a series of resource restrictions?

A)resource mix
B)resource restriction
C)product restriction
D)resource allocation
E)product mix

Question 65

What is the increase in the objective value if 2 units of additive is added?

A)0
B)4
C)12
D)16
E)Not enough information provided

Question 66

Consider the following linear programming problem: The maximum possible value for the objective function is

A)360.
B)480.
C)1520.
D)1560.
E)None of the above

Question 67

Consider the following constraints from a linear programming problem: 2X + Y ≤ 200
X + 2Y ≤ 200
X,Y ≥ 0
If these are the only constraints,which of the following points (X,Y)cannot be the optimal solution?

A)(0,0)
B)(0,200)
C)(0,100)
D)(100,0)
E)(66.67,66.67)

Question 68

Which of the following is not an assumption of LP?

A)certainty
B)proportionality
C)divisibility
D)multiplicativity
E)additivity

Question 69

Consider the following linear programming problem: Which of the following points (X,Y)is feasible?

A)(50,40)
B)(30,50)
C)(60,30)
D)(90,20)
E)None of the above

Question 70

Consider the following linear programming problem: This is a special case of a linear programming problem in which

A)there is no feasible solution.
B)there is a redundant constraint.
C)there are multiple optimal solutions.
D)this cannot be solved graphically.
E)None of the above

Question 71

In order for a linear programming problem to have multiple solutions,the solution must exist

A)at the intersection of the non-negativity constraints.
B)on a non-redundant constraint parallel to the objective function.
C)at the intersection of the objective function and a constraint.
D)at the intersection of three or more constraints.
E)None of the above

Question 72

In order for a linear programming problem to have a unique solution,the solution must exist

A)at the intersection of the non-negativity constraints.
B)at the intersection of a non-negativity constraint and a resource constraint.
C)at the intersection of the objective function and a constraint.
D)at the intersection of two or more constraints.
E)None of the above

Question 73

Consider the following linear programming problem: Which of the following points (X,Y)is feasible?

A)(10,120)
B)(120,10)
C)(30,100)
D)(60,90)
E)None of the above

Question 74

Consider the following linear programming problem: This is a special case of a linear programming problem in which

A)there is no feasible solution.
B)there is a redundant constraint.
C)there are multiple optimal solutions.
D)this cannot be solved graphically.
E)None of the above

Question 75

Which of the following functions is not linear?

A)5X + 3Z
B)3X + 4Y + Z - 3
C)2X + 5YZ
D)Z
E)2X - 5Y + 2Z

Question 76

What is the increase in the objective value if 2 units of packaging are added?

A)11
B)18
C)22
D)36
E)Not enough information provided

Question 77

Which of the following constraints are binding?

A)Extrusion only
B)Packing only
C)Additive only
D)Extrusion and Packaging
E)All constraints are binding

Question 78

Which of the following is not one of the steps in formulating a linear program?

A)Graph the constraints to determine the feasible region.
B)Define the decision variables.
C)Use the decision variables to write mathematical expressions for the objective function and the constraints.
D)Identify the objective and the constraints.
E)Completely understand the managerial problem being faced.

Question 79

Consider the following linear programming problem: Which of the following points (X,Y)is in the feasible region?

A)(30,60)
B)(105,5)
C)(0,210)
D)(100,10)
E)None of the above

Question 80

Consider the following constraints from a linear programming problem: 2X + Y ≤ 200
X + 2Y ≤ 200
X,Y ≥ 0
If these are the only constraints,which of the following points (X,Y)cannot be the optimal solution?

A)(0,0)
B)(0,100)
C)(65,65)
D)(100,0)
E)(66.67,66.67)